The solution to the HJB equation (REF ) for the cost-to-go function \(J({\bf x},t)\)  and the artificial selection \({\bf u}^*({\bf x},t)\)  can be complex time- and state-dependent functions, described by non-linear evolutionary operators (Appendix ). Here, we consider a class of control problems, known as “path integral control" [1]}, [2]}, [3]}, where the cost matrix \(B\)  for artificial intervention with evolution is inversely proportional to the phenotypic covariance \(K\) , i.e., \(B = \lambda K^{-1}\) , where \(\lambda \)  is a constant that determines the overall cost of artificial selection. This assumption implies that imposing artificial selection on highly conserved phenotypes is more costly than on variable phenotypes. This is intuitive as conserved phenotypes are often essential for viability of an organism and it is best to design a control cost function that limits the access to such phenotypes through artificial selection.
